Lessons from academia - Can someone explain that Remark? (FRM part 2)


Hi @David Harper CFA FRM, Hi All, - hope you are doing well.
I'm having a hard time understanding these 2 statements from the Lessons from academia chapter of the FRM (apologies if this is a double but i did not find the answer on the forum)

1. The highlighted blue statement says that counterparty credit risk can be more than double on doubling a position size which violates positive homogeneity(I agree with that). But the same remark , then indicates that this is just misunderstanding and that the risk is a random variable with a wider probability distribution? For me this is ambiguous. How is this not still a violation of homogeneity?
2. Moreover I'm unable to understand what they mean by a composed mapping from position to numbers below (red arrow)?Are they speaking about all risk measures or just VaR? I'm not sure to understand that statement


Thank you very much for any help you can provide